We review here the notion of a shadow, which can be viewed as an axiomatization of \(\mathrm {THH}\) . Shadows first appeared in [1]}, though [2]} is our main reference. Topological Hochschild homology (\(\mathrm {THH}\) ) was originally defined for ring spectra [3]}, but was then generalized to spectral categories, i.e., categories enriched over a monoidal model category of spectra \(\mathcal {S}p\)  [4]}.
